M-Matrices as covariance matrices of multinormal distributions

AbstractThe class of multivariate normal densities n(0, Σ) whose inverse covariance matrix Σ)−1 is an M-matrix is equivalent to this normal density being multivariate totally positive of order 2(MTP2). Equivalent characterizations are given in terms of certain partial correlation coefficients being positive. It is further shown that related partial and multiple regression coefficients and canonical correlation are positive. When Σ is an M-matrix the corresponding normal random vector components are negatively associated. This concept and some extensions are discussed